Group action invariants
| Degree $n$ : | $16$ | |
| Transitive number $t$ : | $1188$ | |
| Parity: | $-1$ | |
| Primitive: | No | |
| Nilpotency class: | $5$ | |
| Generators: | (1,15)(2,16)(3,13,4,14)(5,10,8,11)(6,9,7,12), (1,6,3,7)(2,5,4,8)(9,15,10,16)(11,13)(12,14), (1,8,4,6)(2,7,3,5)(9,14)(10,13)(11,16,12,15) | |
| $|\Aut(F/K)|$: | $2$ |
Low degree resolvents
|G/N| Galois groups for stem field(s) 2: $C_2$ x 7 4: $C_4$ x 4, $C_2^2$ x 7 8: $D_{4}$ x 12, $C_4\times C_2$ x 6, $C_2^3$ 16: $D_4\times C_2$ x 6, $C_2^2:C_4$ x 12, $C_4\times C_2^2$ 32: $C_2^2 \wr C_2$ x 4, $C_2^3 : C_4 $ x 12, $C_2 \times (C_2^2:C_4)$ x 3 64: 16T76 x 6, 16T79 128: 16T240 x 3 256: 16T537 x 2, 16T581 512: 64T? Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$ x 3
Degree 4: $C_2^2$
Degree 8: $C_2^3: C_4$
Low degree siblings
16T1188 x 15, 32T36132 x 8, 32T36133 x 64, 32T36134 x 16, 32T36135 x 16, 32T36136 x 8, 32T36137 x 8, 32T42952 x 8, 32T50812 x 16Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy Classes
There are 52 conjugacy classes of elements. Data not shown.
Group invariants
| Order: | $1024=2^{10}$ | |
| Cyclic: | No | |
| Abelian: | No | |
| Solvable: | Yes | |
| GAP id: | Data not available |
| Character table: Data not available. |